1r(r+12)=-7

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Solution for 1r(r+12)=-7 equation:


Simplifying
1r(r + 12) = -7

Reorder the terms:
1r(12 + r) = -7
(12 * 1r + r * 1r) = -7
(12r + 1r2) = -7

Solving
12r + 1r2 = -7

Solving for variable 'r'.

Reorder the terms:
7 + 12r + 1r2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 12r + 1r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 12r + -7 + r2 = 0 + -7

Reorder the terms:
7 + -7 + 12r + r2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 12r + r2 = 0 + -7
12r + r2 = 0 + -7

Combine like terms: 0 + -7 = -7
12r + r2 = -7

The r term is 12r.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12r + 36 + r2 = -7 + 36

Reorder the terms:
36 + 12r + r2 = -7 + 36

Combine like terms: -7 + 36 = 29
36 + 12r + r2 = 29

Factor a perfect square on the left side:
(r + 6)(r + 6) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(r + 6) equal to 5.385164807 and -5.385164807.

Subproblem 1

r + 6 = 5.385164807 Simplifying r + 6 = 5.385164807 Reorder the terms: 6 + r = 5.385164807 Solving 6 + r = 5.385164807 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 5.385164807 + -6 Combine like terms: 6 + -6 = 0 0 + r = 5.385164807 + -6 r = 5.385164807 + -6 Combine like terms: 5.385164807 + -6 = -0.614835193 r = -0.614835193 Simplifying r = -0.614835193

Subproblem 2

r + 6 = -5.385164807 Simplifying r + 6 = -5.385164807 Reorder the terms: 6 + r = -5.385164807 Solving 6 + r = -5.385164807 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -5.385164807 + -6 Combine like terms: 6 + -6 = 0 0 + r = -5.385164807 + -6 r = -5.385164807 + -6 Combine like terms: -5.385164807 + -6 = -11.385164807 r = -11.385164807 Simplifying r = -11.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.614835193, -11.385164807}

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